Remove admin menu items Header and Background from Twenty Ten Child

I want to simply remove the links to Header and Background from the Appearance menu in the admin for a Twenty Ten child theme. I know I can just comment them out in the Twenty Ten functions.php but that defeats the purpose of using a child theme in the first place.

Is there something I can add to my child theme functions.php that basically says “ignore what Twenty Ten is allowing you to do and don’t add those links”?

(note: I only want to remove the links, no need to remove anything else.)

The Twenty Ten functions.php calls the Background function with onlyadd_custom_background(); with no arguments, nothing to leave empty. It simply turns on the built in functionality in WP3.0. This gets passed through my child theme. What I’d like to do is set up a road block in my child theme functions.php.
Is there an argument I could add that would tell my child theme to ignore this function?

In the meantime I’ve converted the theme to a standalone instead of a child theme to solve the issue but it’s not my first choice.